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March 2, 2015 11:10
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Generates all Clebsh Gordan coefficients starting from a given j1 and j2 and outputs a html file. How to use: ./Clebsch-Gordan.py 0.5 0.5 > output.html
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| #!/usr/bin/env python3 | |
| """ | |
| Generates all Clebsh Gordan coefficients starting from a given j1 and j2 and | |
| outputs a html file. How to use: | |
| ./Clebsch-Gordan.py 0.5 0.5 > output.html | |
| Ward Poelmans <wpoely86@gmail.com> (2014) | |
| """ | |
| import sys | |
| import numpy as np | |
| import scipy.misc as sc | |
| import math | |
| import fractions | |
| def factorial(n): | |
| if n < 0: | |
| return -100000000000 | |
| else: | |
| return math.factorial(n) | |
| # return sc.factorial(n, exact=False) | |
| def clebsh(j1,j2,j,m): | |
| z = 0 | |
| a = 0.0 | |
| b = 0.0 | |
| c = 0.0 | |
| l = "" | |
| for m1 in np.arange(-j1-1,(j1+1)): | |
| for m2 in np.arange(-j2-1,(j2+1)): | |
| #These are just some conditions which need to give zero. | |
| if (m1 + m2) != m: | |
| d = 0 | |
| elif (j1 - j2 - m)%1 != 0.0: | |
| d = 0 | |
| elif (j1 - j2 + m)%1 != 0.0: | |
| d = 0 | |
| else: | |
| c = 0.0 | |
| z = 0 | |
| #This is the algorithm itself, Not very pretty, but that is what it is. | |
| at = ((factorial(j1+j2-j)*factorial(j1-j2+j)*factorial(-j1+j2+j))) | |
| an = (factorial(j1+j2+j+1.0)) #**.5 | |
| a = math.sqrt(at/an) | |
| b = (factorial(j1+m1)*factorial(j1-m1)*factorial(j2+m2)*factorial(j2-m2)*factorial(j-m)*factorial(j+m)) #**.5 | |
| while z<(j1-m1+3): | |
| ct = ((-1.0)**(z+j1-j2+m)) | |
| cn = (factorial(z)*factorial(j1+j2-j-z)*factorial(j1-m1-z)*factorial(j2+m2-z)*factorial(j-j2+m1+z)*factorial(j-j1-m2+z)) | |
| c += ct/cn; | |
| z += 1 | |
| pre = ((-1.0)**(j1-j2+m)) | |
| presqrt = (2.0*j+1.0) | |
| d = pre*math.sqrt(presqrt)*math.sqrt(at/an)*math.sqrt(b)*c | |
| if abs(d)> .0001: | |
| breuk = fractions.Fraction(int(at*b*presqrt*c*c),int(an)).limit_denominator(10000) | |
| pre_str = "-" if pre < 0 else "" | |
| l += "\n<tr><td><math><mn>%s</mn></math></td><td><math><mn>%s</mn></math></td><td><math><mn>%s</mn> <msqrt><mfrac><mn>%s</mn><mn>%s</mn></mfrac></msqrt></math></td></tr>" % (m1,m2,pre_str,breuk.numerator,breuk.denominator) | |
| return l | |
| if len(sys.argv) != 3: | |
| print("Usage: %s j1 j2" % sys.argv[0]) | |
| sys.exit(0) | |
| j1 = float(sys.argv[1]) | |
| j2 = float(sys.argv[2]) | |
| print("<html>\n<title>Clebsch Gordan</title>\n<body>\n<div>\n") | |
| for j in np.arange(abs(j1-j2),j1+j2+1): | |
| for m in np.arange(0,j+1): | |
| print("<math><msub><mi>j</mi><mn>1</mn></msub>=<mn>%s</mn></math> <math><msub><mi>j</mi><mn>2</mn></msub>=<mn>%s</mn></math> <math>j=<mn>%s</mn></math> <math>m=<mn>%s</mn></math><br/>\n" % (fractions.Fraction(j1), fractions.Fraction(j2), fractions.Fraction(j), fractions.Fraction(m))) | |
| print("<table border=1>") | |
| print("<thead><tr> <th><math><msub><mi>m</mi><mn>1</mn></msub></math></th> <th><math><msub><mi>m</mi><mn>2</mn></msub></math></th> </tr></thead>\n") | |
| print("%s" % clebsh(j1,j2,j,m)) | |
| print("</table><br/><br/>\n") | |
| print("</div>\n</body>\n</html>") | |
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